A201997 a(n) is the decimal value of the binary vector used to select terms of A075058 whose sum is n.

0, 1, 2, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 16, 17, 18, 20, 21, 22, 23, 24, 25, 26, 32, 33, 34, 36, 37, 38, 39, 40, 41, 42, 44, 45, 46, 48, 49, 50, 52, 53, 54, 55, 56, 57, 58, 60, 64, 65, 66, 68, 69, 70, 71, 72, 73, 74, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87

Offset

0,3

Links

Table of n, a(n) for n=0..66.

Wikipedia, "Complete" sequence. [Wikipedia calls a sequence "complete" (sic) if every positive integer is a sum of distinct terms. This name is extremely misleading and should be avoided. - N. J. A. Sloane, May 20 2023]

Formula

Binary(a(n)) x A075058 = n, where x is the inner product and the binary vector is in ascending powers of 2 with infinite trailing zeros.

Example

For n=22, the binary vector when applied to A075058 is {0,1,0,1,1,0,...}, consequently 2+7+13=22. The decimal value of the binary vector (in ascending powers of 2) is 26, so a(22)=26.

Mathematica

prevprime[n_Integer] := (j=n; If[n==1, 1, While[!PrimeQ[j], j--]; j]); aprime[n_Integer] := (aprime[n]=prevprime[Sum[aprime[m], {m, 0, n - 1}] + 1]); gentable[n_Integer] := (m=n; ptable={0}; While[m!=0, (i=0; While[aprime[i]<=m && ptable[[i + 1]]!=1, (AppendTo[ptable, 0]; i++)]; ptable[[i]] = 1; m = m - aprime[i - 1])]; ptable); decimal[n_Integer] := (gentable[n]; Sum[2^(k-1)*ptable[[k]], {k, 1, Length[ptable]}]); aprime[0]=1; Table[decimal[r], {r, 0, 100}]

Crossrefs

Cf. A007924, A066352, A200947, A075058.

Sequence in context: A183297 A047573 A039246 * A358225 A039158 A030771

Adjacent sequences: A201994 A201995 A201996 * A201998 A201999 A202000

Keyword

nonn,base,more

Author

Frank M Jackson, Dec 07 2011

Extensions

Edited by N. J. A. Sloane, May 20 2023

Status

approved